Final Answer:
After 83 seconds, the concentration of A is 0.0729 M and the concentration of B is 0.0729 M.
Step-by-step explanation:
The reaction is:
AB(aq) → A(aq) + B(aq)
The rate law for this reaction is:
rate = k[AB]
where:
k is the rate constant
[AB] is the concentration of AB
We can use the following equation to relate the concentration of AB to the concentrations of A and B:
[AB] = [A] - [B]
where:
[A] is the concentration of A
[B] is the concentration of B
Substituting this equation into the rate law, we get:
rate = k([A] - [B])
We can also use the following equation to relate the change in the concentration of A to the change in the concentration of B:
Δ[A] = -Δ[B]
where:
Δ[A] is the change in the concentration of A
Δ[B] is the change in the concentration of B
Substituting this equation into the rate law, we get:
rate = k[A]
This equation is separable, which means that we can separate the variables and integrate both sides of the equation. The integrated form of the equation is:
ln[A] = -kt + ln[A0]
where:
[A] is the concentration of A at time t
[A0] is the initial concentration of A
k is the rate constant
t is the time
We can solve for k by substituting the following values into the equation:
[A] = 0.120 M
[A0] = 0.0729 M
t = 83 s
Solving for k, we get:
k = -0.00120 s^-1
Now we can use the equation to calculate the concentration of A after 83 seconds:
ln[A] = -(-0.00120 s^-1) * 83 s + ln(0.120 M)
Solving for [A], we get:
[A] = 0.0729 M
Therefore, after 83 seconds, the concentration of A is 0.0729 M and the concentration of B is 0.0729 M.